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My research

My name is Valeria Korkishko. I graduated from Donetsk National University in 2014. Now I’m a post-graduate student of the Faculty of Physics and Technology. I’m a teacher of physics. I really love my job, I love the process of sharing my knowledge with other people. But I also have interests in science. My special subject is Computational Fluid Dynamics. My research deals with principals of modeling pulse and wave flows with mobile borders.

I’m particularly interested in application of Mac-Cormack method to the high pulse fluid flows. One of the first tasks is to verify and if possible to amplify knowledge of possibility of application Mac-Cormack method to hydrodynamics method. I have been working at the problem for two years. I got interested in it when I was a student. My present work is based on the theory developed by my scientific adviser Alexandr Nikolaevich Semko. He has PHD at technical sciences. The title of his doctor’s dissertation was “Pulse and wave flows of liquid with mobile borders”. He proved it in 2006. Ten years after the problem hasn’t lost its topical significance.

The title of my future dissertation is “Computational modeling of high pulse processes and technologies”. Pulse and wave flows with mobile borders meet in many physical processes bound to short-term and intensive influence on fluid, such as impact, explosion, electrical discharge etc. Dimensional redistribution of energy takes place in such kind of processes. It leads to sharp local increase of energy density. This effect is widely used in different installations and technological processes. Essential features of such processes are fugacity, high pressure, wave character and cavitation. Such flows are described by equations of non-stationary gas dynamics with appropriate initial and boundary conditions. Boundary conditions are often put on the specific borders. Motion laws of such borders are not known in advance and are a part of the decision of a problem.

All these factors essentially complicate the decision of such issues. Therefore working out of the mathematical models adequately reflecting pulse and wave flows of fluid with mobile borders and cavitation is still the actual problem to which my research is devoted.

Computational Fluid Dynamics (CFD) provides a qualitative (and sometimes even quantitative) prediction of fluid flows by means of mathematical modeling (partial differential equations), numerical methods (discretization and solution techniques) and software tools (solvers, pre- and post-processing utilities). CFD uses a computer to solve the mathematical equations for the problem at hand. At present there is a growing interest in improving the accuracy of numerical methods. CFD is a highly interdisciplinary research area, which lies at the interface of physics, applied mathematics and computer science.

In computational fluid dynamics, the Mac-Cormack method is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. Mac-Cormack in 1969. The Mac-Cormack method is very elegant and easy to understand and program. It was this which first attached my notice. It is well suited for nonlinear equations (inviscid Burgers equation, Euler equations, etc.) Unlike first-order upwind scheme, the Mac-Cormack does not introduce diffusive errors in the solution. However, it is known to introduce dispersive errors in the region where the gradient is high. In my research the theory of flux-corrected transport (FCT) developed by Boris and Book is extended to the numerical Mac-Cormack method in order to minimize dispersive errors. It has been established by recent studies that Mac-Cormacks method can be adequately applied to calculate liquid flows. So the scientific validity of my job is application of Mac-Cormack method, widely used in gas dynamics, to liquid dynamics.

My research is based on several steps. Initially, one must make mathematical model. Secondly, generation of cells, time instants, space and time discretization comes. Main part is software implementation and post-processing visualization. And after verification of model, the certain issues can be solved. Now I got more results in theoretical part rather than in practical use of obtained data. The obtained results agree with the previous findings.The problems are still far from being completely understood.

I’m planning to finish my research work by the end of my study at the post-graduate course. I hope to get the degree of Candidate of Technical Science. By this time I will have got some publications in scientific periodicals. I think my dissertation will make a certain contribution to the knowledge of the subject by the discovery of new facts about the effectivity of Mac-Cormack’s method being applied to high pulse flows with mobile borders.